Bulletin of Mathematical Biology

, Volume 77, Issue 10, pp 1934–1954 | Cite as

Estimating Tumor Growth Rates In Vivo

  • Anne Talkington
  • Rick DurrettEmail author
Original Article


In this paper, we develop methods for inferring tumor growth rates from the observation of tumor volumes at two time points. We fit power law, exponential, Gompertz, and Spratt’s generalized logistic model to five data sets. Though the data sets are small and there are biases due to the way the samples were ascertained, there is a clear sign of exponential growth for the breast and liver cancers, and a 2/3’s power law (surface growth) for the two neurological cancers.


Tumor growth kinetics Gompertz Logistic Power law growth 



This work was begun during an REU in the summer of 2013 associated with an NSF Research Training Grant at Duke University in mathematical biology. Both authors were partially supported by DMS 1305997 from the probability program at NSF. They would also like to thank Natalia Komarova, Marc Ryser, and referees #2 and #3 who made a number of helpful suggestions.


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Copyright information

© Society for Mathematical Biology 2015

Authors and Affiliations

  1. 1.Department of MathDuke UniversityDurhamUSA

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